Program for cube sum of first n natural numbers

Print the sum of series 13 + 23 + 33 + 43 + …….+ n3 till n-th term.

Examples :

Input : n = 5
Output : 225
13 + 23 + 33 + 43 + 53 = 225

Input : n = 7
Output : 784
13 + 23 + 33 + 43 + 53 + 
63 + 73 = 784

A simple solution is to one by one add terms.

C++

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// Simple C++ program to find sum of series
// with cubes of first n natural numbers
#include <iostream>
using namespace std;
  
/* Returns the sum of series */
int sumOfSeries(int n)
{
    int sum = 0;
    for (int x = 1; x <= n; x++)
        sum += x * x * x;
    return sum;
}
  
// Driver Function
int main()
{
    int n = 5;
    cout << sumOfSeries(n);
    return 0;
}

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Java

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// Simple Java program to find sum of series
// with cubes of first n natural numbers
  
import java.util.*;
import java.lang.*;
class GFG {
  
    /* Returns the sum of series */
    public static int sumOfSeries(int n)
    {
        int sum = 0;
        for (int x = 1; x <= n; x++)
            sum += x * x * x;
        return sum;
    }
  
    // Driver Function
    public static void main(String[] args)
    {
        int n = 5;
        System.out.println(sumOfSeries(n));
    }
}
  
// Code Contributed by Mohit Gupta_OMG <(0_o)>

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Python3

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# Simple Python program to find sum of series
# with cubes of first n natural numbers
  
# Returns the sum of series 
def sumOfSeries(n):
    sum = 0
    for i in range(1, n + 1):
        sum += i * i*i
          
    return sum
  
   
# Driver Function
n = 5
print(sumOfSeries(n))
  
# Code Contributed by Mohit Gupta_OMG <(0_o)>

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C#

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// Simple C# program to find sum of series
// with cubes of first n natural numbers
using System;
  
class GFG {
    /* Returns the sum of series */
    static int sumOfSeries(int n)
    {
        int sum = 0;
        for (int x = 1; x <= n; x++)
            sum += x * x * x;
        return sum;
    }
  
    // Driver Function
    public static void Main()
    {
        int n = 5;
        Console.Write(sumOfSeries(n));
    }
}
// This code is contributed by
// Smitha Dinesh Semwal

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PHP

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<?php
// Simple PHP program to find sum of series
// with cubes of first n natural numbers
  
// Returns the sum of series 
function sumOfSeries( $n)
{
    $sum = 0;
    for ($x = 1; $x <= $n; $x++)
        $sum += $x * $x * $x;
    return $sum;
}
  
// Driver code
$n = 5;
echo sumOfSeries($n);
  
// This Code is contributed by vt_m.
?>

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Output :

225

Time Complexity : O(n)

An efficient solution is to use direct mathematical formula which is (n ( n + 1 ) / 2) ^ 2

For n = 5 sum by formula is
       (5*(5 + 1 ) / 2)) ^ 2
          = (5*6/2) ^ 2
          = (15) ^ 2
          = 225

For n = 7, sum by formula is
       (7*(7 + 1 ) / 2)) ^ 2
          = (7*8/2) ^ 2
          = (28) ^ 2
          = 784

C++

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// A formula based C++ program to find sum
// of series with cubes of first n natural
// numbers
#include <iostream>
using namespace std;
  
int sumOfSeries(int n)
{
    int x = (n * (n + 1) / 2);
    return x * x;
}
  
// Driver Function
int main()
{
    int n = 5;
    cout << sumOfSeries(n);
    return 0;
}

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Java

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// A formula based Java program to find sum
// of series with cubes of first n natural
// numbers
  
import java.util.*;
import java.lang.*;
class GFG {
    /* Returns the sum of series */
    public static int sumOfSeries(int n)
    {
        int x = (n * (n + 1) / 2);
  
        return x * x;
    }
  
    // Driver Function
    public static void main(String[] args)
    {
        int n = 5;
        System.out.println(sumOfSeries(n));
    }
}
  
// Code Contributed by Mohit Gupta_OMG <(0_o)>

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Python3

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# A formula based Python program to find sum
# of series with cubes of first n natural 
# numbers
  
# Returns the sum of series 
def sumOfSeries(n):
    x = (n * (n + 1/ 2)
    return (int)(x * x)
  
  
   
# Driver Function
n = 5
print(sumOfSeries(n))
  
# Code Contributed by Mohit Gupta_OMG <(0_o)>

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C#

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// A formula based C# program to 
// find sum of series with cubes
// of first n natural numbers
using System;
  
class GFG {
      
    // Returns the sum of series
    public static int sumOfSeries(int n)
    {
        int x = (n * (n + 1) / 2);
  
        return x * x;
    }
  
    // Driver Function
    public static void Main()
    {
        int n = 5;
          
        Console.Write(sumOfSeries(n));
    }
}
  
// Code Contributed by nitin mittal.

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PHP

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<?php
// A formula based PHP program to find sum
// of series with cubes of first n natural
// numbers
  
function sumOfSeries($n)
{
    $x = ($n * ($n + 1) / 2);
    return $x * $x;
}
  
// Driver Function
$n = 5;
echo sumOfSeries($n);
  
// This code is contributed by vt_m.
?>

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Output:

225

Time Complexity : O(1)

How does this formula work?
We can prove the formula using mathematical induction. We can easily see that the formula holds true for n = 1 and n = 2. Let this be true for n = k-1.

Let the formula be true for n = k-1.
Sum of first (k-1) natural numbers = 
            [((k - 1) * k)/2]2

Sum of first k natural numbers = 
          = Sum of (k-1) numbers + k3
          = [((k - 1) * k)/2]2 + k3
          = [k2(k2 - 2k + 1) + 4k3]/4
          = [k4 + 2k3 + k2]/4
          = k2(k2 + 2k + 1)/4
          = [k*(k+1)/2]2

The above program causes overflow, even if result is not beyond integer limit. Like previous post, we can avoid overflow upto some extent by doing division first.

C++

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// Efficient CPP program to find sum of cubes
// of first n natural numbers that avoids
// overflow if result is going to be withing
// limits.
#include <iostream>
using namespace std;
  
// Returns sum of first n natural
// numbers
int sumOfSeries(int n)
{
    int x;
    if (n % 2 == 0)
        x = (n / 2) * (n + 1);
    else
        x = ((n + 1) / 2) * n;
    return x * x;
}
  
// Driver code
int main()
{
    int n = 5;
    cout << sumOfSeries(n);
    return 0;
}

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Java

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// Efficient Java program to find sum of cubes
// of first n natural numbers that avoids
// overflow if result is going to be withing
// limits.
import java.util.*;
import java.lang.*;
class GFG {
    /* Returns the sum of series */
    public static int sumOfSeries(int n)
    {
        int x;
        if (n % 2 == 0)
            x = (n / 2) * (n + 1);
        else
            x = ((n + 1) / 2) * n;
        return x * x;
    }
  
    // Driver Function
    public static void main(String[] args)
    {
        int n = 5;
        System.out.println(sumOfSeries(n));
    }
}
// Code Contributed by Mohit Gupta_OMG <(0_o)>

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Python3

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# Efficient Python program to find sum of cubes 
# of first n natural numbers that avoids 
# overflow if result is going to be withing 
# limits.
  
# Returns the sum of series 
def sumOfSeries(n):
    x = 0
    if n % 2 == 0
        x = (n / 2) * (n + 1)
    else:
        x = ((n + 1) / 2) * n
          
    return (int)(x * x)
  
   
# Driver Function
n = 5
print(sumOfSeries(n))
  
# Code Contributed by Mohit Gupta_OMG <(0_o)>

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C#

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// Efficient C# program to find sum of 
// cubes of first n natural numbers 
// that avoids overflow if result is
// going to be withing limits.
using System;
  
class GFG {
      
    /* Returns the sum of series */
    public static int sumOfSeries(int n)
    {
        int x;
        if (n % 2 == 0)
            x = (n / 2) * (n + 1);
        else
            x = ((n + 1) / 2) * n;
        return x * x;
    }
      
    // Driver code
    static public void Main ()
    {
        int n = 5;
        Console.WriteLine(sumOfSeries(n));
    }
}
  
// This code is contributed by Ajit.

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PHP

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<?php
// Efficient PHP program to 
// find sum of cubes of first  
// n natural numbers that avoids
// overflow if result is going 
// to be with in limits.
  
// Returns sum of first n 
// natural numbers
function sumOfSeries($n)
{
    $x;
    if ($n % 2 == 0)
        $x = ($n / 2) * ($n + 1);
    else
        $x = (($n + 1) / 2) * $n;
    return $x * $x;
}
  
// Driver code
$n = 5;
echo sumOfSeries($n);
  
// This code is contributed by vt_m.
?>

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Output:

225

This article is contributed by R_Raj. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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